Tree Networks with Causal Structure

P. Bialas; Z. Burda; J. Jurkiewicz; A. Krzywicki

doi:10.1103/physreve.67.066106

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Tree Networks with Causal Structure

P. Bialas·Z. Burda·J. Jurkiewicz·A. Krzywicki

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Abstract

Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree graphs, an analytically solvable case. General formulae are derived, describing the degree distribution, the ancestor-descendant correlation and the probability a randomly chosen node lives at a given geodesic distance from the root. It is shown that the Hausdorff dimension $d_H$ of the causal networks is generically infinite, in contrast to the maximally random trees, where it is generically finite.

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P. Bialas, Z. Burda, J. Jurkiewicz, A. Krzywicki. 2003-03-28. Tree Networks with Causal Structure. https://doi.org/10.1103/physreve.67.066106

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